# Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies

arXiv: https://arxiv.org/abs/2609.13201 · HTML: https://mlsanity.com/paper/2609.13201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 13 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [Dataset Decomposition: Faster LLM Training with Variable Sequence Length Curriculum](https://mlsanity.com/paper/2405.13226/) (2024)

## Abstract (arXiv)

Training datasets for upcoming LLMs would include a significant amount of AI text/image data generated from current LLMs. In such a scenario, it is important to understand how this affects batch decompositions and thereby, the performance of the resultant new LLM. In this paper, we consider AI generated data as anomalies ``linked" to main data points and study decomposition and undersampling properties of the overall random dataset. We use redundancy graphs and iteration techniques to obtain bounds for the minimum size of a strongly dissimilar (SD) decomposition and demonstrate a phase transition phenomena, wherein the minimum size is essentially determined by the main data points when the number of anomalies is small and is ``taken" over by the anomalies above a certain threshold. We also establish a size criticality result for the strong similarity of a randomly undersampled dataset and illustrate our results with examples involving categorical datasets, whose overall space size is much larger than the size of the dataset.